Question

Please help me with this problem​

Answer 1

Answer:

The measures of angles A, B, and C are respectively 21°, 125°, and 34°

Step-by-step explanation:

Equations

We are given some conditions applying to the internal angles on a triangle ABC.

The measure of angle A is 13 less than the measure of angle C.

The measure of angle B is 11 less than 4 times the measure of angle C

Let x = measure of angle C

The first conditions states:

$m\angle A = x-13$

The second conditions states:

$m\angle B = 4x-11$

The sum of all angles must be 180°, thus:

$x - 13 + 4x - 11 + x = 180$

Simplifying:

6x -24 = 180

Adding 24:

6x = 204

Dividing by 6:

x = 204/6

x = 34

$m\angle C = x = 34^\circ$

$m\angle B = 4x-11 = 4*34-11 = 125^\circ$

$m\angle A = x - 13 = 34 - 13 = 21^\circ$

The measures of angles A, B, and C are respectively 21°, 125°, and 34°